Electron beam lithography (“e-beam” lithography) involves exposing a film of polymer resist, which resides on a substrate, to a beam of electrons, thereby breaking the molecular chains of the exposed polymer. In the case of a positive resist, the exposed portions of the polymer have increased solubility with respect to a solvent, so that by bringing the solvent into contact with the exposed portions, selective dissolution or etching of the resist takes place to produce empty spaces such as trenches or voids in the resist. By filling the spaces with metal and then removing the remaining (unexposed) resist, metallic structures can be fabricated that are suitable for various microelectronic applications. Advanced photolithographic masks and test structures are generally fabricated using electron beam lithography.
Since the resist is sensitive to the deposition of energy resulting from interactions with electrons as they pass through the resist, the resolution achievable with electron beam lithography is, to a first approximation, limited by the spot size of the incident e-beam. In reality, however, electron scattering causes a broadening of the exposed region beyond the spot size. One form of broadening is known as “forward scattering”, and occurs as the electrons scatter at small angles as they pass through the resist. This is illustrated in FIG. 1, which shows an incident e-beam 20 that enters a resist 26 located over a substrate 32. The incident beam 20 within the resist 26 experiences inelastic scattering events 36 (as well as elastic scattering events), which result in secondary electrons being created and the beam being deflected. The increase in effective beam diameter in nanometers due to forward scattering is given empirically by the formula df=0.9 (Rt/Vb)1.5, where Rt is the resist thickness in nanometers and Vb is the beam voltage in kilovolts. Thus, forward scattering can be mitigated by using the thinnest possible resist and the highest available accelerating voltage. Although this broadening effect is important for thick resists, it is relatively unimportant for thin resists at high beam energies. Moreover, the broadening that arises from this kind of scattering is often small compared to the intrinsic resolution of the resist.
A second, more vexing form of scattering involving electrons is also illustrated in FIG. 1. After the beam 20 has entered the substrate 32, it may undergo various elastic scattering events 40, 42, 44 (as well as inelastic scattering events), and recoil back through the substrate 32 at a large angle before returning to the resist 26. These so-called “backscattered” electrons arise as follows. Once the electrons of the beam 20 enter the substrate 32, they undergo a series of scattering events during which they lose energy before eventually coming to a stop. For the range of energies typically used in electron beam lithography systems, i.e., 20–100 keV, the total path length may be hundreds of microns. The electron scattering can be elastic, resulting in a change of direction, or it can be inelastic, resulting in both a change of direction and the creation of a secondary electron. Generally, the scattering angle is larger with elastic scattering than it is with inelastic scattering.
Moreover, between scattering events, the various energy loss processes experienced by an electron can be accurately described by a continuous energy loss mechanism (the so-called “continuous slow-down approximation”; see, for example, H. A. Bethe, Handbook of Physics, vol. 24, Springer, Berlin, 1933), which results in energy being deposited in the material through which the electron is moving. As a result of all these physical phenomena, the resist 26 will be “exposed”—and thereby have energy deposited in it—over a cross sectional area many orders of magnitude greater than just the spot size of the electron beam 20 where it enters the resist 26; this is often referred to as the cause of proximity effects. When defining complex patterns in a resist, the proximity effects must be corrected for by reducing the direct exposure, in order to maintain the degree of pattern fidelity (i.e., lack of deviation from the intended pattern) that is required for advanced prototyping and mask making. The distribution of energy deposited in the resist 26 as a function of distance from the incident beam spot can be simulated using Monte-Carlo methods.
There is a wealth of literature on Monte Carlo simulation techniques in books and journals, such as the Journal of Vacuum Science and Technology, in particular, each year's November/December issue. (See, for example, C. R. K. Marrian et al., J. Vac. Sci. Technol., B14, pp. 3864–3869, 1996; and D. F. Kyser and N. S. Viswanathan, J. Vac. Sci. Technol., vol. 12, pp. 1305–1308, 1975. See also R. J. Hawryluk et al., J. Appl. Phys, 45, p. 2551–2566, 1974; R. Shimizu et al., Rep. Prog. Phys., 55, pp. 487–531, 1992; and Z.-J. Ding et al., Scanning, 18, p. 92–113, 1996.) Numerous approaches have been employed to correct for proximity effects. However, they are all plagued by the fact that mathematically, the correction of proximity effects is an ill-posed problem, since a complete solution requires the application of negative exposure doses to the resist (i.e., conceptually, energy must be removed from the resist), which is physically unrealizable. This results in solutions being non-ideal and computationally extremely intensive, which is a problem that is exacerbated by the ever shrinking minimum feature sizes of micro and nano electronic circuits.
Exposure of the resist 26 to backscattered electrons ultimately limits the density at which small features can be written. To illustrate this, consider the case of forming an array of dots in a resist. To do this, the electron beam would be held long enough at a given dot position to achieve the desired exposure, and then moved on to the next dot position. As demonstrated by Kyser and Viswanathan (supra), however, it is known that each time such a dot position is exposed, the resist surrounding the dot position may experience an exposure equal to about 10−4 of the total dose (i.e., the total net deposited energy) out to a distance of more than 5 microns from the intended exposure site; this may be viewed as a “blurring” of the feature. As the density of dots is increased, however, to the point where the number of dots within a 5 micron radius approaches 104, the indirect exposure (“blurring” effect) becomes comparable to the direct exposure. In this example, this point is reached as the dot spacing approaches 90 nm, for a square array. Attempts to further increase the density become increasingly difficult, as the processing window shrinks rapidly.
Accordingly, proximity effects severely limit the ability of electron beam lithography to form dense structures. One way to mitigate this problem would be to use membranes or extremely thin substrates. However, membranes have very limited applicability to microelectronics manufacturing, because they cannot be made large enough nor can they withstand the processing needed to form complex structures.
What is needed is a method of reducing proximity effects that can be employed on solid substrates. The present invention satisfies this need by significantly reducing the root cause of the problem, namely, the deposition of energy by electrons in the resist at positions away from the point of impact of the incident electron beam. This not only reduces the amount of extraneous exposure, but also the lateral extent over which it occurs, thereby significantly reducing the computation required for correction of the proximity effects in those cases where it is still required.